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What is the measure of the largest angle of triangle ABC if BC=9 , AC=10 and AB=13 ?

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guteskind | Student | eNotes Newbie

Posted May 7, 2011 at 8:19 PM via web

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What is the measure of the largest angle of triangle ABC if BC=9 , AC=10 and AB=13 ?

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giorgiana1976 | College Teacher | Valedictorian

Posted May 7, 2011 at 8:26 PM (Answer #1)

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Since the lengths of the 3 sides are given, we'll use the law of cosines to determine the measure of the largest angle.

The largest angle is the opposite angle to the largest length of triangle. Since the length of AB is the largest, then the measure of the angle C has to be determined.

cos C = (BC^2 + AC^2 - AB^2)/2BC*AC

We'll replace the sides by its lengths:

cos C = (81 + 100 - 169)/180

cos C = 12/180

cos C = 1/15

cos C = 0.067

C = 86.2 degrees

The measure of the largest angle of triangle ABC is: C = 86.2 degrees.

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